The problem of obtaining an image of phase from an image of intensity has been considered during the last twenty years. In <<Relationship between two-dimensional intensity and phase in Fresnel Diffraction zone>>, Abramoshkin et al. (1989) provide the value of the phase gradient from intensity, the intensity gradient and Green's functions in an infinite space.
More precisely, Fornaro et al. discloses in <(<Interferometric SAR phase unwrapping Using Green's Formulation>> using the Fast Fourier Transforms for computing the phase from phase gradient by using Green's functions.
The formulation using the Fourier Transform is used in WO 00/26622, which describes the process of obtaining such a phase image. That process concerns the retrieval of phase of a radiation wave field by solving the equation of the energy transfer. The rate of variation of the intensity of the image is determined first, orthogonally with respect to the surface that spans the wave field (i.e., when measuring the intensity in the two separate surfaces). This rate is then subject to the following computation process: defining an integral transform, multiplication by a filter corresponding to the inversion of the differential operator, and defining the inverse integral transform. The result is multiplied by the function of intensity with respect to the surface. The filters have the form based on the characteristics of the optical system used for acquiring the intensity data, such as the numerical aperture and spatial frequencies.
More specifically, the Fourier transform is the Fourier transform in two dimensions.
However, one of the major problems in the field of image processing is the computation time for applications involving solution of the equations characteristic to the image.
Thus, the computation times are not sufficient to perform the computations for a large number of images.
Further, it should be noted that WO '622 does not mention the boundary conditions, by supposing that the phase is zero at infinity.